If ( 4y - 4over y ) = 11 then, find the value of ( y ² + 1over y ² ).

If ( 4y - 4over y ) = 11 then, find the value of ( y ² +…

If ( ${4y - {4\over y}}$ ) = 11 then, find the value of ( ${y ^ 2 + {1\over y ^ 2}}$ ).

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $9{9\over 16}$ .

( ${4y - {4\over y}}$ ) = 11

⇒ ${y - {1\over y}}$ = $11 \over 4$

Squaring both sides

⇒ ( ${y - {1\over y}}$ )² = ( $11 \over 4$ )²

⇒ y² + $1\over y^2$ - 2 = $121 \over 16$

⇒ y² + $1\over y^2$ = $153 \over 16$ = $9{9\over 16}$